A particle moving in the xy plane undergoes a displacement `vec(S) =( 2.0 hat(i) + 3.0hat(J) )m` while a constant
force `vec(F) = (5.0 hat(1) + 2.0 hat(j) ) ` N acts on the particle.
(a) Calculate the magnitude of the displacement and that of the force.
(b) Calculate the work done by the force

Explanation

`vec(s) = (2.0hat(i) + 3 hat(j)) " " vec(F) = (5.0 hat(i) + 2.0hat(j))`
`|vec(s)| = sqrt(x^(2) +y^(2)) = sqrt((2.0)^(2) + (3.0)^(2)) = sqrt(13) m `
`|vec(F)| = sqrt(F_(x)^(2) + F_(y)^(2)) = sqrt( (5.0)^(2) + (2.0)^(2)) = 5.4N`
(b) Work done by force, W = `vec(F).vec(s)`
`= (5.0hat(i) + 2.0hat(j)).(2.0hat(i) + 3.0hat(j)) N.m`
`= 10 + 0 + 0 + 6 = 16`N.m = 16 J